It's Trivial?

Algebra Level 5

Let \(a_n\) be defined such that it is the arithmetic mean of the p numbers before it. Let \(a_i=i, 1 \leq i \leq p\).Let \(a_\infty=b_p\) for such a sequence.If

\(\sum_{p=0}^{20} b_p {20 \choose p}=a*b^c\)

Then find \(a+b+c\)

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